Mathematical modelling of nucleation and growth of crystals with buoyancy effects

被引：15

作者：

Alexandrov, D. V. ^{[1
]}

机构：

[1] Ural Fed Univ, Dept Math Phys, Ekaterinburg, Russia

来源：

PHILOSOPHICAL MAGAZINE LETTERS | 2016年 / 96卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

Nucleation; crystal growth; buoyancy; INTERMEDIATE STAGE; CRYSTALLIZATION; SOLIDIFICATION; KINETICS; CONVECTION; EVOLUTION; MELT;

D O I：

10.1080/09500839.2016.1177222

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A complete analytical solution of the integro-differential model describing the nucleation of crystals and their subsequent growth in a binary system with allowance for buoyancy forces is constructed. An exact analytical solution of the Fokker-Planck-type equation for the three-parameter density distribution function is found for arbitrary nucleation kinetics. Two important cases of the Weber-Volmer-Frenkel-Zel'dovich and Meirs kinetics are considered in some detail. It is shown that the solute concentration decreases and the distribution function increases with increasing the melt supercooling (with increasing the depth of a metastable system). It is demonstrated that the distribution function attains its minimum at a certain size of crystals owing to buoyancy forces.

引用

页码：132 / 141

页数：10

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